{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "主要内容:  \n",
    "\n",
    "- 模型过拟合和欠拟合\n",
    "- 模型的成本和成本函数定义\n",
    "- 评价模型的标准\n",
    "- 学习曲线,以及用学习去了来对模型进行诊断\n",
    "- 通用的模型优化方案\n",
    "- 其他模型评价标准"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.过拟合和欠拟合\n",
    "\n",
    "过拟合是指模型能很好的你和训练样本,但对新数据的预测准确性很差.  \n",
    "欠拟合是指模型不能很好的拟合训练样本.且对新数据的预测准确性也不好."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_dots=20\n",
    "x=np.linspace(0,1,n_dots)\n",
    "y=np.sqrt(x)+0.2*np.random.rand(n_dots)-0.1\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_polynomial_fit(x, y, order):\n",
    "    p = np.poly1d(np.polyfit(x, y, order))\n",
    "\n",
    "    # 画出拟合出来的多项式所表达的曲线以及原始的点\n",
    "    t = np.linspace(0, 1, 200)\n",
    "    plt.plot(x, y, 'ro', t, p(t), '-', t, np.sqrt(t), 'r--')\n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(18, 4))\n",
    "titles = ['Under Fitting', 'Fitting', 'Over Fitting']\n",
    "models = [None, None, None]\n",
    "for index, order in enumerate([1, 3, 10]):\n",
    "    plt.subplot(1, 3, index + 1)\n",
    "    models[index] = plot_polynomial_fit(x, y, order)\n",
    "    plt.title(titles[index], fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "左边是欠拟合,(高偏差),右边是过拟合,(高方差),[虽然模型对测试数据集的拟合很好,但是在新数据的预测上会很差]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.成本函数\n",
    "\n",
    "成本是衡量模型与训练样本符合程度的指标.简单的说,成本是针对所有的训练样本,模型拟合出来的值和训练样本的真实值的误差平均值.而成本函数就是成本与模型参数的函数关系.模型的训练过程,就是找出合适的模型参数,使得成本函数的值最小.成本函数记为$ J(\\Theta ) $. 其中 $\\Theta $表示模型参数."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "总结来说,针对一个数据集,可以选择很多模型来拟合数据,一旦选定了某个模型,就需要从这个模型的无穷多个参数来选择一个最优参数.使得成本函数最小."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.模型准确性\n",
    "\n",
    "测试数据集的成本,即$ J_{test}(\\Theta) $是评估模型准确性的最值观指标.他的值越小,说明模型预测出来的值与真实的值差异越小.对新数据的预测准确性就越好,需要特别注意的是,用来测试模型准确性的测试数据集必须是模型\"没见过的数据\".[对数据划分训练集和测试集]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 1.模型性能的不同表达方式 \n",
    "\n",
    "在sklearn里,使用的是分数来表达(0~1之间),数值越大,说明准确性越好.  \n",
    "模型的准确性和成本成反比,准确性越高,成本越低.\n",
    "\n",
    "- 2.交叉验证数据集\n",
    "\n",
    "另一个更科学的方式是把数据集分成三份,分别是训练数据集,交叉验证数据集,测试数据集.(推荐比例是6:2:2).  \n",
    "在模型选择的时,我们使用训练数据集来训练算法参数,用交叉验证来验证参数.选择交叉验证成本$ J_{cv}(\\Theta) $最小的多项式作为数据拟合模型.最好再用测试集来测试准确性  \n",
    "**因为在模型的选择中,我们使用了交叉验证数据集,所以筛选的模型多项式阶数d的过程中,实际上并没有使用测试数据集,这样包装了使用测试数据集来计算成本行列模型的准确性,我们的模型是没有\"见过\"测试数据.也就是说,测试数据集没有参与模型选择的过程]**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.学习曲线\n",
    "\n",
    "我们可以通过$ J_{test}(\\Theta) $ 和 $ J_{cv}(\\Theta)$作为纵坐标,画出与训练数据集m的带线啊哦关系,这就是学习曲线.通过学习曲线,可以值观的观测模型的准确性和训练数据集大小的关系.  \n",
    "流程:  \n",
    "- 把数据集划分为训练集和交叉验证数据集.\n",
    "- 取训练数据集的20%作为训练样本,训练出模型参数.\n",
    "- 使用交叉验证集来计算训练出来的模型准确性.\n",
    "- 以训练集的准确性,交叉验证的准确性作为纵坐标,训练集个数作为横坐标.在坐标轴上画出上述步骤计算出来的准确性.\n",
    "- 训练数据集增加10%,继续画图发现.\n",
    "\n",
    "学习曲线要表达的内容是,当训练数据增加时,模型对训练数据集拟合的准确性以及对交叉验证数据集预测的准确性的变化规律."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=np.linspace(0,1,200)\n",
    "y=np.sqrt(X)+0.2*np.random.rand(200)-0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=X.reshape(-1,1)\n",
    "y=y.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 构造一个多项式模型.使用pipeline来构造,(流水线),这个流水线里可以包含多个数据处理模型,前一个模型处理完,就可以处理下一个.\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polynomal_model(degree=1):\n",
    "    polynomal_feature=PolynomialFeatures(degree=degree,include_bias=False)\n",
    "    linear_regression=LinearRegression()\n",
    "    pipeline=Pipeline([(\"polynomial_features\",polynomal_feature),(\"linear_regression\",linear_regression)])\n",
    "    return pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import learning_curve\n",
    "from sklearn.model_selection import ShuffleSplit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_learning_curve(estimator,title,X,y,ylim=None,cv=None,n_jobs=1,train_sizes=np.linspace(.1,1.0,5)):\n",
    "    plt.title(title)\n",
    "    if ylim is not None:\n",
    "        plt.ylim(*ylim)\n",
    "    plt.xlabel(\"Training examples\")\n",
    "    plt.ylabel(\"Score\")\n",
    "    train_sizes,train_scores,test_scores=learning_curve(estimator,X,y,cv=cv,n_jobs=n_jobs,train_sizes=train_sizes)\n",
    "    train_scores_mean=np.mean(train_scores,axis=1)\n",
    "    train_scores_std=np.std(train_scores,axis=1)\n",
    "    test_scores_mean=np.mean(test_scores,axis=1)\n",
    "    test_scores_std=np.std(test_scores,axis=1)\n",
    "    plt.grid()\n",
    "    \n",
    "    plt.fill_between(train_sizes,test_scores_mean-train_scores_std,train_scores_mean+train_scores_std,alpha=0.1,color='r'\n",
    "                    )\n",
    "    plt.fill_between(train_sizes, test_scores_mean - test_scores_std,test_scores_mean + test_scores_std, alpha=0.1, color=\"g\")\n",
    "    plt.plot(train_sizes, train_scores_mean, 'o--', color=\"r\",label=\"Training score\")\n",
    "    plt.plot(train_sizes, test_scores_mean, 'o-', color=\"g\",label=\"Cross-validation score\")\n",
    "\n",
    "    plt.legend(loc=\"best\")\n",
    "    return plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 为了让学习曲线更平滑，交叉验证数据集的得分计算 10 次，每次都重新选中 20% 的数据计算一遍\n",
    "cv = ShuffleSplit(n_splits=10, test_size=0.2, random_state=0)\n",
    "titles = ['Learning Curves (Under Fitting)',\n",
    "          'Learning Curves',\n",
    "          'Learning Curves (Over Fitting)']\n",
    "degrees = [1, 3, 10]\n",
    "\n",
    "plt.figure(figsize=(18, 4))\n",
    "for i in range(len(degrees)):\n",
    "    plt.subplot(1, 3, i + 1)\n",
    "    plot_learning_curve(polynomal_model(degrees[i]), titles[i], X, y, ylim=(0.75, 1.01), cv=cv)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 过拟合和欠拟合的特征\n",
    "\n",
    "- 过拟合: 模型对训练数据集的准确性较高,其成本比较低,对交叉验证数据集的准确性比较低.\n",
    "- 欠拟合:模型对训练数据集的准确性比较低,其成本比较高,对交叉验证数据集的准确性也比较低.\n",
    "\n",
    "一个好的机器学习算法应该是对讯息了数据集准确性高,成本低,既能较准确的拟合数据,对交叉验证数据集准确性高,成本低.误差小,也就是对未知数据具有良好的预测性."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 算法模型的性能优化\n",
    "- 如果是过拟合,可以采取的性能如下:\n",
    "    - 获取更多的训练数据:更多的数据可以改善过拟合问题.\n",
    "    - 减少输入的特征数量:减少模型的计算量,复杂度\n",
    "    \n",
    "- 如果是欠拟合.说明模型过于简单,需要增加模型的复杂度.\n",
    "    - 增加有价值的特征:重新解读并理解数据.\n",
    "    - 增加多项式特征:有时候,从已知的数据里挖掘出更多的特征是不太容易的,这个时候,可以使用纯数学的方案增加多项式特征.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 查准率和查全率\n",
    "\n",
    "- 查准率(Precision)\n",
    "- 召回率(Recall)\n",
    "\n",
    "$$\n",
    "Precision=\\frac{TruePositive}{TruePositive+FalsePositive}\n",
    "$$\n",
    "\n",
    "$$\n",
    "Recall=\\frac{TruePositive}{TruePositive+FlaseNegative}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## F1 Score\n",
    "$$\n",
    "F_1Score=2\\frac{PR}{P+R}\n",
    "$$\n",
    "P:查准率,R:查全率."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {
    "height": "241px",
    "width": "364px"
   },
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
